On the m-capacitated peripatetic salesman problem with capacity restrictions

We consider a special case of the problem of finding m Hamiltonian cycles with capacity restrictions on the number of usages of the edges (m-Capacitated Peripatetic Salesman Problem or m-CPSP): the minimization and maximization 2-CPSP with edge weights chosen from an integer segment {1, q} with the edges capacities given as independent identically distributed random variables equal to 2 with probability p and 1 with probability (1 ? p). Some polynomial algorithms are proposed for 2-CPSP_min and 2-CPSP_max with average performance guarantees. In particular, when the edge weights are equal to 1 and 2, the algorithms have approximation ratios (19 ? 5p)/12 and (25 + 7p)/36 for the minimization and the maximization problem correspondingly.     

The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis

We present algorithms for singular spectrum analysis and local approximation methods used to extrapolate time series. We analyze the advantages and disadvantages of these methods and consider the peculiarities of applying them to various systems. Based on this analysis, we propose a generalization of the local approximation method that makes it suitable for forecasting very noisy time series. We present the results of numerical simulations illustrating the possibilities of the proposed method.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 148–159, January, 2005.     

Theory of the generalized collision integral. IV

In the maximum time interval of kinetic evolution of the single-particle distribution function of a spatially homogeneous system summation of the step diagrams (without intersections of the lines of propagation and interaction) is carried out for an arbitrary nonequilibrium state in the Markov limit, as well as for a local equilibrium state with regard for memory effects. Procedures are indicated for the step renormalization of diagrams of arbitrary order with respect to the density in the Markov limit, with subsequent ladder renormalization. Ring diagrams with preliminary step and ladder renormalizations are summed. A more correct derivation is given for the generalized Boltzmann (Boltzmann-Landau) collision integrals for dense systems with a strong short-range (as well as strong long-range) potential. It is shown that the step, ring, and ladder renormalizations yield a nondivergent two-particle distribution function in a classical equilibrium plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–91, August, 1978.     

Elliptic and circular dichroism effects in two-photon double ionization of atoms

An ab initio parametrization of the two-photon double ionization amplitude from an s2 subshell of an atom in a 1S state is presented and used to predict two light polarization effects on photoelectron angular distributions that do not exist in single-photon double ionization: (i) elliptic dichroism and (ii) circular dichroism at equal energy sharing. Estimates for He show large magnitudes for these effects, which provide a means for polarization control of double ionization by vacuum ultraviolet light.     

Two-way shape memory in a nanoscale sample of Ti49.5Ni25.5Cu25.0 alloy with a partially ordered structure

The dependence of the thermomechanical properties and structure of rapidly quenched Ti_49.5Ni_25.5Cu_25.0 alloy on the annealing conditions has been studied. A sample with a partially ordered structure is found to have two-way shape memory effect during single deformation. An alloy sample 17 × 10 × 0.07 μm in size has been prepared and trained. It is shown to demonstrate two-way shape memory behavior.     

Influence of photon energy on the efficiency of photochemotherapy

It is found that when indotricarbocyanine dye in HeLa cells is exposed to photons with different energies the efficiency of cell damage is wavelength independent provided the photosensitizer absorbs the same number of photons per unit time. In vivo animal experiments with two strains of tumor show that when the wavelength of the irradiating light is increased (668, 740, and 780 nm) and the number of photons absorbed per unit time per unit volume of the tumors is held constant, the damage depth increases by a factor of 1.5 and 3, respectively. The observed changes are related both to differences in the in vivo tissue optical transmission with increasing wavelength and an increased local concentration of oxygen owing to photodissociation of oxyhemoglobin.     

Calcium-containing cathodic material for solid oxide fuel cells

Using the citrate sol-gel method, a new complex oxide Ca_0.75Y_0.25Co_0.15Mn_0.85O_2.92 is synthesized. It is shown that this compound is crystallized in the rhombically distorted version of perovskite structure (a = 0.53397(8), b = 0.7470(1), c = 0.52810(6) nm). The phase is characterized by a low coefficient of thermal expansion (CTE) (13.8 ppm K^?1) and high electric conductivity (135 S/cm at 900°C). The chemical reaction between Ca_0.75Y_0.25Co_0.15Mn_0.85O_2.92 and the YSZ and GDC electrolyte materials is studied. The material is highly reactive and reacts with YSZ and GDC at 900°C and 1070°C, respectively. It is concluded that Ca_0.75Y_0.25Co_0.15Mn_0.85O_2.92 is a promising cathodic material for solid oxide fuel cells, provided a reliable protection SDC sublayer is formed between the cathode and the YSZ membrane.     

X‐ray diffraction refinement of the crystal structure of anosovite prepared from leucoxene

The crystal structure of anosovite, (Ti_1.69Al_0.26Fe_0.05)³⁺(Ti_0.97Zr_0.03)⁴⁺O₅, prepared by carbothermal reduction of leucoxene under vacuum at 1450°C has been refined by Rietveld method using powder X‐ray diffraction data. It was found that it represents slightly monoclinically deformed pseudobrookite type structure with lattice parameters a = 9.8111 Å, b = 3.7509 Å, c = 9.9468 Å, β = 90.628°. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)